# T Test for Independent Samples

In the area of statistics, the t- test is the most commonly used method that is used for the purpose of studying the difference in means between the two groups. In theoretical terms, the application of t – test is even possible when the sample size is relatively very small. The pre requisite is that variables have to be normally distributed within each group and there is not reliably different variation of scores within the groups. It is possible to evaluate the normality assumption within each group by looking at the data distribution through histograms or by means of performing a test of normality. The equality of the variances can also be verified by the use of an F test. More difficult and complicated tests like the Levene’s test can also be used. If the data is found to be not distributed normally then the difference in the mean gets evaluated between groups by the use of non-parametric alternative techniques to t- test.

The p- level or p-value that comes with a t test output gives out the probability of error that is a part of the acceptance or rejection of the hypotheses about the existence of the difference. This probability of error helps  in deciding about the acceptance or rejection of  the null hypotheses which talks about no difference between the categories of observation.  Some researchers also suggest that if the difference is in the direction that is predicted, then only one half of the probability distribution is considered. However, the contradictory view to this is that always the standard two tailed test probability should be reported.

The data arrangement in t test for independent samples calls imperatively for one independent grouping variable and one dependent variable are called for. The means of the dependent variable will be compared between the chosen groups on the specified values of the independent variable.

In practical research, it so happens that more than two groups need to be compared or take up a comparison of groups that has been created by more than one independent variable. In this case we use analysis of variance. It is a generalisation of t test. When we talk of only two groups then ANOVA would give identical results to t test